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Strategic Approaches for CAT Success: Ranking & Derrangements, One-word Substitution - Day 38

Strategic Approaches for CAT Success: Ranking & Derrangements, One-word Substitution - Day 38

Edited By Irshad Anwar | Updated on Sep 20, 2023 04:31 PM IST | #CAT

Hello CAT 2023 candidates,

The CAT exam 2023 for MBA admissions 2024–2026 will be held on November 26. In this CAT 2023 60-day preparation guide series of Careers360, we will discuss the strategies on Derangement and Ranking Arrangement Questions for day 38 that can help you prepare well and crack the CAT entrance test 2023.

This article includes Ranking arrangement questions, one-word substitution MCQs, and Logical deduction meaning. Aspirants can go through the article below for further practice questions on Ranking arrangement questions, one-word substitution questions and logical deduction questions. CAT Preparation 2023 in 60 days

Strategic Approaches for CAT Success: Ranking & Derrangements, One-word Substitution - Day 38
Strategic Approaches for CAT Success: Ranking & Derrangements, One-word Substitution - Day 38

Part-1: Quantitative Aptitude for CAT exam

CAT Exam Important Topic: Strategy to Prepare “Permutations and Combinations (Ranking and Derangements)” and ranking arrangement questions

Important Concept/Formula Used in Derangement

Problems on Derangement and Ranking

  1. Finding of Rank of a word in a dictionary with no alphabet is repeating: See link in references
  2. Finding the Rank of a word (if letters are repeating): See link in references
  3. Concept of Derangements: permutation of the elements of a certain set in a way that no element of that set appears in their original positions.
  4. The number of derangements of a set with n objects is given by the formula

1695205886483

CAT Exam: Previous Year CAT Questions On Permutations and Combinations (Ranking and Derangements)

Q1. All the rearrangements of the word "DEMAND" are written without including any word that has two D's appearing together. If these are arranged alphabetically, what would be the rank of "DEMAND"? [CAT PYQ]

A. 36 B. 74 C. 42 D. 86

Ranking Arrangement Questions With Answers: (B)

Total words formed from the word DEMAND = 6! /2! = 360

Total words formed from the word DEMAND where 2 D’s appear together = 5! = 120

Total words formed from the word DEMAND where 2D’s do not appear together =

360 – 120 = 240

Words starting with ‘A’, without two D’s adjacent to each = Words starting with A - Words starting with A where 2 D’s are together

⇒ Words starting with ‘A’, without two D’s adjacent to each = 5!/2! - 4! = 36.

Next letter is D (in alphabetical order from the letters of the word DEMAND)

Words starting with DA: 4! words = 24 words

Words starting with DEA = 3! = 6 words

Words starting with DEA = 3! = 6 words

Words starting with DEMA

=> First word is DEMADN

=> Second is DEMAND

Rank of DEMAND = 36 + 24 + 6 + 6 + 2 = 74

Derangement and Ranking

Q2. In how many ways can you put 6 letters into their respective envelopes such that exactly 4 go into the right envelope? [CAT Sample Question]

a) 24 b) 102 c)15 d) 530

Ranking Arrangement Questions With Answers: (C)

No of ways in which the 4 correct envelopes can be selected= 6C4 =15

Derangement of the remaining 2 envelopes & letters =

1695205886361

= 2! (1 -1 + ½) = 1

Total No of ways of arrangement = 1 x 15= 15.

CAT entrance exam: Prerequisite to Derangement

  1. Factorial

  2. Fundamental Principle of counting,

  3. Concept of Selection and Arrangement

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Tips and Tricks of Ranking Arrangement Questions for CAT

  1. For nCr to be greatest,

    • if n is even, r = n/2
    • if n is odd, r = (n + 1)/2 or (n – 1)/2
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  1. Number of squares in a square of n × n side = 12 + 22 + 32 + 42 + … n2

  2. Number of rectangles in a square of n × n side = 13 + 23 +33 + 43 + … n3. (This includes the number of squares.)

  3. Practice sample papers and questions based on previous years CAT Questions.

  4. Do not spend much time on this.

CAT study material: References to Study (Theory) Derangement and Ranking

  1. NCERT Class 11 Maths
  2. Concept Tree (YouTube, Link: https://www.youtube.com/watch?v=A4Fp-vP243k)
  3. CAT Funda (YouTube, Link: https://www.youtube.com/watch?v=QCqj1ijqp8w)

CAT study material: References to Practice ranking arrangement questions

  1. How to prepare quantitative Aptitude for CAT by Arun Sharma.
  2. (CAT PYQs https://www.youtube.com/watch?v=P0UQxxR_slc)

Part-2: CAT 2023 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)

CAT 2023 Syllabus Topic: Strategy to prepare “Logical Deduction” for CAT

Important Concepts/ Formulas used in Logical Deduction

Middle term: It is the term common to both the premise and is denoted by ‘M’.

Major premise: The premise in which the middle term is in place of the predicate is called a major premise.

Minor premise: The premise in which the middle term is in the place of the subject is called a minor premise.

Subject vs Predicate: Consider this question statement

  1. All cats are dogs
  2. Some dogs are birds
  3. No bird is a pig
  4. Some pigs are not birds.
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In all such statements, the first term is called the subject and the second is called the predicate.

CAT Exam: Previous years Questions on Logical Deduction from CAT/ MBA Entrance Exam:

Q1. Statements: No Arc is Circle. Some Arc are Triangles.

Conclusions:

Square are Circles

Some Triangles are Circles.

  1. The only conclusion I follow

  2. Only conclusion II follows

  3. Either I or II follows

  4. Neither I nor II follows

  5. Both I and II follow

Solution: [D]

Statement I is negative.

Statemnet II is negative.

Therefore Negative conclusion must be there.

But neither conclusion is negative.

Logical Deduction Questions

Q2. The question contains six statements, followed by four options of combinations of any three of the given sentences. Choose the option in which the combinations are logically related. Consider the first two as statements and the third as conclusions:

Statements:

  1. Some pinks are colour.
  2. No Blue is black.

Conclusions:

  1. All pink are spark.
  2. Some sparks are not E.
  3. Some yellow are black.
  4. Some pink are black.

1. ABD 2. ABF 3. CDE 4. BCF 5. NOT

Solution: (5)

Option

Statement 1

Statement 2

Conclusion

Remark

1

A (+ve)

B (-ve)

D (-ve)

True

2

A (+ve)

B (-ve)

F (+ve)

False

3

C (+ve)

D (-ve)

E(+ve)

False

4

B (-ve)

C (+ve)

F (+ve)

False

We must check option (1) only (rest are false); No common term is there A and B, so no conclusion can be drawn.

Hence answer is (5)

CAT entrance exam: Prerequisite

  1. Syllogism
  2. Venn Diagram

Tips and Tricks for CAT Logical Deduction Questions

  1. There should be three and only three distinct terms between two premises for the conclusion to be obtained.

  2. The middle term should be distributed at least once on the premises for the conclusion to be obtained.

Statement 1

Statement 2

Remark

Positive

Positive

+ve Conclusion

Positive

Negative

-ve Conclusion

Negative

Positive

-ve Conclusion

Negative

Negative

No Conclusion

  1. Learn the rule of distribution (See References to Study Link)

  2. Practice Sample Papers.

References to CAT Study (Theory) Logical Deduction

  1. LRDI by Nikhil K. Sinha
  2. Concept Tree (YouTube link: https://www.youtube.com/watch?v=lkyRADOwUuY)
  3. (YouTube link: https://www.youtube.com/watch?v=lsl5y8xlqCw&t=442s)

References to Practice Logical Deduction questions

  1. Verbal and Non-Verbal Reasoning by R S Agrawal.
  2. MBA Entrance Previous years Papers and Sample Papers.

Part-3: CAT Exam Preparation 2023: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)

CAT Exam Important Topic: Strategy to Prepare “One Word Substitution” and one word substitution questions for competitive exams such as CAT-2023

CAT Tips and Tricks for One Word Substitution Questions:

  1. Divide the One-word substitutions into the categories like

One Word Substitution for Study

Some Examples:

Printing using a stone or a metal plate with a completely smooth surface

Lithography

Mapping of earth and its formation

Geography

Words used for people with various qualities, habits, and abilities.

Some Examples:

The doctor who attends to corn in the feet and hands

Chiropodist

The doctor who deals with the female reproductive system

Gynecologist

Words for likes and dislikes

Some Examples:

One who loves and admires the British

Anglophile

One who loves without seriousness

Philanderer

Words used for practices & beliefs

Some Examples:

One who believes in many Gods

Polytheist

One who believes that God is the union of all forces of the universe

Pantheist

Words used for various kinds of killings

Some Examples:

the killing of a whole race

Genocide

The killing of a newborn child

Infanticide

There can be more categories like this.

  1. Remember the following factors while choosing a word for a sentence

  • Contextual
  • Grammatical
  • Tone of sentence
  • Insight
  1. Learning more about substitution will be helpful.

  1. Practice Sample questions.

CAT Previous Years' Questions on One Word Substitution MCQs

Sample Questions:

Directions: Choose the best substitute from the given options for highlighted phrase

Q.1. We visited the ancient palace yesterday, there we saw old manuscripts written by saints, we tried but it was not clear enough to be read.

  1. Corrigible
  2. Legible
  3. Negligible
  4. Illegible

Ans: [4]

One word substitution quiz with answers

Q.2. They organized a house party for Sara’s birthday but she does not get excited easily even if you put in a lot of effort and emotion.

  1. Gregarious
  2. Placid
  3. Inclement
  4. Frenzied

Ans: [2]

CAT 2023: Prerequisite to one word substitution MCQs

  1. Sentence Structure
  2. Vocabulary
  3. Parts of Speech

CAT exam: References to Study (Theory)

  1. One word substitution questions for competitive exams
  2. Wren and Martin
  3. (https://www.youtube.com/watch?v=3YPMi1RbSb0)

CAT exam: References to Practice one word substitution questions

  1. one-word substitution MCQs
  2. Verbal Ability for CAT by Arun Sharma and Meenakshi Upadhyay.
  3. CAT Previous years Papers and other MBA Entrance Exams.
  4. (youTube; Link: https://www.youtube.com/watch?v=1DU9ZWbGvLs)

Practice and remain focused, and we'll be back tomorrow with Day 39.

Thank you! All the best!

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Questions related to CAT

Have a question related to CAT ?

Hello aspirant,

A bachelor's degree from an accredited university with a CGPA of at least 50% (or an aggregate of 45% for the SC, ST, and PwD/DA categories) is required in order to appear in the CAT exam in 2024. Duration and manner of degree: The course needs to last three years. The mode might be online, distant, or regular.

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Hope this information helps you.

Hello student

As a self-employed individual with your own cafe, you'll need to provide documents that establish your business and work experience. Here are some documents you can prepare for your CAT application:


1. *Business Registration Documents*:

- Partnership Deed (already have)

- Business PAN Card (already have)

- FSSAI License (already have, though it's in your partner's name)

2. *Proof of Business Ownership*:

- Affidavit or declaration stating your ownership and role in the cafe

- Business registration certificate (if you have one)

3. *Proof of Work Experience*:

- A letter or certificate from your partner or co-owner confirming your work experience and role in the cafe

- A detailed resume highlighting your entrepreneurial journey and responsibilities

4. *Financial Documents*:

- Income Tax Returns (ITRs) for the last 2-3 years (if applicable)

- Balance Sheets and Profit & Loss statements for your cafe (if audited)

5. *Rental Agreement*:

- Already have, but ensure it's updated and signed


Additional tips:


- Ensure all documents are scanned and uploaded in the required format (usually PDF or JPEG)

- Keep your documents organized and easily accessible for the application process

- Be prepared to provide additional information or clarification if requested by the admission authorities


Remember to check the specific requirements for each B-school you're applying to, as they may vary. Good luck with your CAT application!

Hello aspirant,
The CAT exam syllabus is not officially prescribed, but it generally includes topics from the following sections:

1. Verbal Ability and Reading Comprehension (VARC)
2. Data interpretation and logical reasoning
3. Quantitative ability

  • Arithmetic

  • Algebra

  • Geometry and Mensuration

  • Number System

  • Modern Math

It seems unlikely that you would be able to get admission in the BTech CS branch at BIT Sindri or Mesra with a CML rank of 2058 and category rank of 433.

Key points:

1. The search results indicate that a CML (Common Merit List) rank of 2058 is quite low for admission to premier engineering colleges like BIT Sindri or NIT Mesra.

2. The cutoff ranks for BTech CS branch at these institutes are usually much higher, often in the range of 1000-2000 for the general category.

3. With a category rank of 433, you may have a better chance of getting admission in the reserved category quota, but the competition is still quite high.

4. The search results do not provide specific cutoff details for BIT Sindri or NIT Mesra, but the general trend suggests your current ranks may not be sufficient for the CS branch in these institutes.

My advice would be to:

1. Check the latest cutoff ranks and admission criteria on the official websites of BIT Sindri and NIT Mesra.

2. Explore other options like state-level engineering colleges or NITs where your current ranks may have a better chance of securing admission.

3. Consider improving your performance in the next attempt of the entrance exam to increase your chances of getting into your desired BTech program.



For VARC, read daily from diverse sources (newspapers, novels, journals) to improve comprehension and vocabulary. Practice RC passages and verbal ability questions regularly. For DILR (Data Interpretation and Logical Reasoning) and QA (Quantitative Aptitude), solve previous years' papers and take mock tests to identify weak areas. Join a coaching institute or online courses for guidance and stay consistent with your study schedule. Review and analyze your performance in mocks to understand mistakes and improve. Maintain a positive mindset and stay disciplined in your preparation.

View All

1-radian measures 600. (True/False)

Option: 1

True


Option: 2

False


$111111^2$ = 

Option: 1

123456654321


Option: 2

123454321


Option: 3

123454321


Option: 4

12345654321


1111112 =___________ 

Option: 1

 123456654321


Option: 2

1234554321


Option: 3

123454321


Option: 4

12345654321


159702 is divisible by

Option: 1

7


Option: 2

9


Option: 3

11


Option: 4

6


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

What best can be said about the number of satellites serving C? 

Option: 1

Must be between 450 and 725 

 


Option: 2

Cannot be more than 800 
 


Option: 3

Must be between 400 and 800 

 


Option: 4

Must be at least 100 


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

What is the minimum possible number of satellites serving B exclusively? 

Option: 1

100


Option: 2

200


Option: 3

500


Option: 4

250


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S? 

Option: 1

At most 475 

 


Option: 2

Exactly 475 
 


Option: 3

At least 475 

 


Option: 4

No conclusion is possible based on the given information 


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

 If the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE? 

Option: 1

The number of satellites serving C cannot be uniquely determined 

 


Option: 2

The number of satellites serving B is more than 1000 
 


Option: 3

All 1600 satellites serve B or C or S 

 


Option: 4

The number of satellites serving B exclusively is exactly 250 


2839155 is divisible by

Option: 1

2


Option: 2

7


Option: 3

55


Option: 4

None of the above


'a' for which x^{2}-ax+9= 0 can be written as square of a linear factor is

Option: 1

6


Option: 2

-6,6


Option: 3

\left ( 6,\infty \right )


Option: 4

\left ( -\infty,-6 \right )


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